6. Solve by factoring. (4 marks)
\[
\begin{array}{l}
x^{2}-5 x-14=0 \\
x^{2}-7 x+2 x-14=0 \\
x^{2} x(x-7)+2(x-7)=0 \\
(x-7)(x+2)=0 \\
(x-7)(x+2)=0 \\
x=7,-2
\end{array}
\]
7. For the following set of data find the mean, median, mode, and standard deviation.
(4 marks)
\[
\begin{array}{lllllllllllllllllllll}
2 & 8 & 11 & 0 & 13 & 1 & 5 & 4 & 6 & 3 & 7 & 12 & 4 & 11 & 5 & 18 & 9 & 2 & 10 & 7 & 4
\end{array}
\]

Answer

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Answer

\(\boxed{\text{Mean: } 6.76, \text{ Median: } 6, \text{ Mode: } 4, \text{ Standard Deviation: } 4.44}\)

Steps

Step 1 ：First, sort the data set: \(0, 1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 12, 13, 18\)

Step 2 ：Calculate the mean: \(\frac{0+1+2+2+3+4+4+4+5+5+6+7+7+8+9+10+11+11+12+13+18}{21} = \frac{142}{21} \approx 6.76\)

Step 3 ：Find the median: The middle value is 6, so the median is \(6\)

Step 4 ：Find the mode: The number 4 appears the most (3 times), so the mode is \(4\)

Step 5 ：Calculate the standard deviation: \(\sqrt{\frac{(0-6.76)^2+(1-6.76)^2+...+(18-6.76)^2}{21}} \approx 4.44\)

Step 6 ：\(\boxed{\text{Mean: } 6.76, \text{ Median: } 6, \text{ Mode: } 4, \text{ Standard Deviation: } 4.44}\)